The distribution of a variable is a description of the relative numbers of times each possible outcome will occur in a number of trials. The function describing the probability that a given value will occur is called the probability density function (abbreviated PDF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).
Formally, a distribution can be defined as a normalized measure, and the distribution of a random variable 
is the measure 
on 
defined by setting
 |
where 
is a probability space, 
is a measurable space,
and 
a measure on 
with 
. If the measure is a Radon
measure (which is usually the case), then the statistical distribution is a generalized function in the sense of a generalized
function.
